estnoise: Estimate noise level

In rdetools: Relevant Dimension Estimation (RDE) in Feature Spaces

Description

Estimates the noise level for a label vector 'y' and a denoised version of this label vector 'yh'. Which loss function is used to estimate the noise level depends on the kind of problem (regression problem or classification problem).

Usage

estnoise(y, yh, regression = FALSE, nmse = TRUE)

Arguments

y	a label vector containg only -1 and 1 for a classification problem, and real numbers in case of regression
yh	a denoised version of y which can be obtained by using e.g. rde
regression	FALSE in case of a classification problem, TRUE in case of a regression problem
nmse	if 'nmse' is TRUE and this is a regression problem, the mean squared error will be normalized

Details

In case of a classification problem, the 0-1-loss is used to estimate the noise level:

y = (y_1, ..., y_n)

L\_01(y, yh) = (1/n)*sum(y != yh)

In case of a regression problem, the mean squared error (mse) or the normalized mean squared error (nmse) is used, depending on whether 'nmse' is FALSE (mse) or TRUE (nmse):

L\_mse = (1/n)*sum( (y - yh)\^2 )

L\_nmse = L\_mse(y, yh) / ((1/n)*sum( (y - (1/n)*sum(y))\^2 )

Value

Estimated noise level

Author(s)

Jan Saputra Mueller

See Also

sincdata, rde_loocv, rde_tcm, rbfkernel, drawkpc

Examples

## estimate noise of sinc data explicitly
d <- sincdata(100, 0.7) # generate sinc data
K <- rbfkernel(d$X) # calculate rbf kernel matrix
r <- rde(K, d$y, est_y = TRUE) # estimate relevant dimension
noise <- estnoise(d$y, r$yh, regression = TRUE) # estimate noise level

## estimate noise of sinc data implicitly (via rde_loocv)
d <- sincdata(100, 0.7) # generate sinc data
K <- rbfkernel(d$X) # calculate rbf kernel matrix
r <- rde(K, d$y, est_y = TRUE) # estimate relevant dimension AND estimate noise
r$noise # estimated noise level

Example output

NULL

rdetools documentation built on May 2, 2019, 7:02 a.m.